I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!

Monday, November 14, 2005

Only four blocks to solve

Molly has a set of four alphabet blocks. Each side of these blocks is printed with a different letter, making 24 in total. Molly notices that by rearranging the blocks, she can spell each of the following words:

From the word EXAM, we conclude that E and A are not on the same block.From the word OGRE, we conclude that E and O are not on the same block.From the word OKAY, we conclude that A and O are not on the same block.Combining these, we conclude that A, E, and O are on different blocks. Assume that A is on block 1, E is on block 2, and O is on block 3.

From the words BOXY and EXAM, we conclude that X is not on the same block as A (block 1), E (block 2), and O (block 3), so X is on block 4.From the words BOXY and OKAY, we conclude that Y is not on the same block as A (block 1), O (block 3), and X (block 4), so Y is on block 2.From the word EXAM, we conclude that M is not on the same block as A (block 1), E (block 2), and X (block 4), so M is on block 3.From the word OKAY, we conclude that K is not on the same block as A (block 1), Y (block 2), and O (block 3), so K is on block 4.From the word BOXY, we conclude that B is not on the same block as Y (block 2), O (block 3), and X (block 4), so B is on block 1.From the words BUCK and JUMP, we conclude that U is not on the same block as B (block 1), M (block 3), and K (block 4), so U is on block 2.From the words PAWN and JUMP, we conclude that P is not on the same block as A (block 1), U (block 2), and M (block 3), so P is on block 4.From the word JUMP, we conclude that J is not on the same block as U (block 2), M (block 3), and P (block 4), so J is on block 1.From the words CHAW and BUCK, we conclude that C is not on the same block as A (block 1), U (block 2), and K (block 4), so C is on block 3.From the words CHAW and PAWN, we conclude that W is not on the same block as A (block 1), C (block 3), and P (block 4), so W is on block 2.From the word CHAW, we conclude that H is not on the same block as A (block 1), W (block 2), and C (block 3), so H is on block 4.From the word PAWN, we conclude that N is not on the same block as A (block 1), W (block 2), and P (block 4), so N is on block 3.

Now, we must still have three letters for block 1, and two letters for each of the blocks 2, 3, and 4. We have the following letters left:

D, F, G, I, L, R, S, T, Z

From the words DIGS, FLIT and GIRL, we conclude that I is not on the same block as D, F, G, L, R, S, and T, so I is on the same block as Z. Furthermore, I and Z are on block 2, 3, or 4.From the word ZEST, we conclude that Z is not on the same block as E (block 2), so Z is on block 3 or 4.From the word OGRE, we conclude that G and R are not on the same block as E (block 2), and O (block 3), so G and R are on block 1 or 4, but not on the same block.From the word GIRL, we conclude that I is not on the same block as G and R (block 1 or 4), so I is on block 2 or 3. Since Z is on block 3 or 4, I and Z must be on block 3. Now we have all six letters of block 3: C, I, M, N, O, and Z.

From the word GIRL, we conclude that L is not on the same block as G and R (block 1 and 4), so L is on block 2.From the words FLIT and GIRL, we conclude that F, G, L, R, and T are not on the same block as L (block 2), and from the word ZEST, we conclude that S is not on the same block as E (block 2). So D must be on block 2.Now we have all six letters of block 2: D, E, L, U, W, and Y.

From the words GIRL and DIGS, we conclude that G is not on the same block as R and S.From the words FLIT and ZEST, we conclude that T is not on the same block as F and S.Combining this, F, R, and S must be on the same block (block 1), and G and T must be on the same block (block 4).

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Monday, November 14, 2005

Only four blocks to solve

Molly has a set of four alphabet blocks. Each side of these blocks is printed with a different letter, making 24 in total. Molly notices that by rearranging the blocks, she can spell each of the following words:

From the word EXAM, we conclude that E and A are not on the same block.From the word OGRE, we conclude that E and O are not on the same block.From the word OKAY, we conclude that A and O are not on the same block.Combining these, we conclude that A, E, and O are on different blocks. Assume that A is on block 1, E is on block 2, and O is on block 3.

From the words BOXY and EXAM, we conclude that X is not on the same block as A (block 1), E (block 2), and O (block 3), so X is on block 4.From the words BOXY and OKAY, we conclude that Y is not on the same block as A (block 1), O (block 3), and X (block 4), so Y is on block 2.From the word EXAM, we conclude that M is not on the same block as A (block 1), E (block 2), and X (block 4), so M is on block 3.From the word OKAY, we conclude that K is not on the same block as A (block 1), Y (block 2), and O (block 3), so K is on block 4.From the word BOXY, we conclude that B is not on the same block as Y (block 2), O (block 3), and X (block 4), so B is on block 1.From the words BUCK and JUMP, we conclude that U is not on the same block as B (block 1), M (block 3), and K (block 4), so U is on block 2.From the words PAWN and JUMP, we conclude that P is not on the same block as A (block 1), U (block 2), and M (block 3), so P is on block 4.From the word JUMP, we conclude that J is not on the same block as U (block 2), M (block 3), and P (block 4), so J is on block 1.From the words CHAW and BUCK, we conclude that C is not on the same block as A (block 1), U (block 2), and K (block 4), so C is on block 3.From the words CHAW and PAWN, we conclude that W is not on the same block as A (block 1), C (block 3), and P (block 4), so W is on block 2.From the word CHAW, we conclude that H is not on the same block as A (block 1), W (block 2), and C (block 3), so H is on block 4.From the word PAWN, we conclude that N is not on the same block as A (block 1), W (block 2), and P (block 4), so N is on block 3.

Now, we must still have three letters for block 1, and two letters for each of the blocks 2, 3, and 4. We have the following letters left:

D, F, G, I, L, R, S, T, Z

From the words DIGS, FLIT and GIRL, we conclude that I is not on the same block as D, F, G, L, R, S, and T, so I is on the same block as Z. Furthermore, I and Z are on block 2, 3, or 4.From the word ZEST, we conclude that Z is not on the same block as E (block 2), so Z is on block 3 or 4.From the word OGRE, we conclude that G and R are not on the same block as E (block 2), and O (block 3), so G and R are on block 1 or 4, but not on the same block.From the word GIRL, we conclude that I is not on the same block as G and R (block 1 or 4), so I is on block 2 or 3. Since Z is on block 3 or 4, I and Z must be on block 3. Now we have all six letters of block 3: C, I, M, N, O, and Z.

From the word GIRL, we conclude that L is not on the same block as G and R (block 1 and 4), so L is on block 2.From the words FLIT and GIRL, we conclude that F, G, L, R, and T are not on the same block as L (block 2), and from the word ZEST, we conclude that S is not on the same block as E (block 2). So D must be on block 2.Now we have all six letters of block 2: D, E, L, U, W, and Y.

From the words GIRL and DIGS, we conclude that G is not on the same block as R and S.From the words FLIT and ZEST, we conclude that T is not on the same block as F and S.Combining this, F, R, and S must be on the same block (block 1), and G and T must be on the same block (block 4).